Question

If a manufacturer sells x units of a certain product, his revenue R and cost C (in dollars) are given by the following.

R = 15x
C = 2000 + 10x + 0.001x2
Use the fact that profit = revenue − cost, to determine how many units the manufacturer should sell to enjoy a profit of at least $1690. (Enter your answer using interval notation.).

Answer 1

To determine the quantity of units the manufacturer should sell to enjoy a profit of at least $1690, we need to find the point where the profit is equal to or greater than $1690. The profit can be calculated by subtracting the cost from the revenue: Profit = Revenue - Cost.

Step-by-step explanation:

To determine the quantity of units the manufacturer should sell to enjoy a profit of at least $1690, we need to find the point where the profit is equal to or greater than $1690. The profit can be calculated by subtracting the cost from the revenue: Profit = Revenue - Cost. Given the revenue function R = 15x and the cost function C = 2000 + 10x + 0.001x^2, we can set up the equation for profit as follows: Profit = 15x - (2000 + 10x + 0.001x^2). To find the quantity of units for the desired profit, we solve the equation Profit ≥ 1690 for x.